Industrial standard muting accomplishes many goals
and I do not claim the simple theory here forms
an analytic basis for it all.
Nevertheless, the concept
that moveout and stack should be pre- and post- multiplied by
weighting functions to make the composite operation quasi-unitary,
provides a theoretical basis for what would otherwise be
an entirely ad hoc process.
Thus, quasi-unitary transformation
(a form of operator preconditioning)
is a mute-like process that should precede
the human intervention of subsequent muting.

The example studied here of Texas gulf coast velocities
is a mild form of the problem of traveltime cross overs,
and this study needs elaboration for the much stronger
velocity contrasts found in many other locations.